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C₂×#13152 #494918

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,13,19,14,21,32,20)(9,22,26,35,10,27,30,38)(11,31,33,17,23,18,12,34)(15,29,16,28,37,25,36,24);(7,9,23,28,32,30,33,29,14,10,11,24,13,26,12,25)(8,15,17,22,19,16,18,35,21,37,34,27,20,36,31,38);(4,6)(7,10,11,28,32,26,12,29,14,9,23,24,13,30,33,25)(8,16,17,35,19,37,18,27,21,36,34,38,20,15,31,22)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402114);